Multiply the following complex numbers: $({-1-i}) \cdot ({3+5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-i}) \cdot ({3+5i}) = $ $ ({-1} \cdot {3}) + ({-1} \cdot {5}i) + ({-1}i \cdot {3}) + ({-1}i \cdot {5}i) $ Then simplify the terms: $ (-3) + (-5i) + (-3i) + (-5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -3 + (-5 - 3)i - 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -3 + (-5 - 3)i - (-5) $ The result is simplified: $ (-3 + 5) + (-8i) = 2-8i $